I don't follow the comics either, and I'm sure there could be good reasons to the contrary, but I would just think that by the 31st century, he would be long dead of old age. I know Kryptonians gain super powers from our yellow sun, But I never got the impression that they were immortal, or even that their lifespan overly exceeded that of humans.
Smallville has suggested it. In one episode they encounter a Meteror Freak who can see how people will die by touching them. When he touches Clark he doesn't see Clark's death but an image of a red cape with a yellow "S-shield" on it flapping in the "wind" against a space/galactic backdrop. The kid says that it "seems as though if you go on forever, Clark, like you never die." -or something to that effect.